(Pythagoras’s Theorem) Prove by vector method that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given:- Right angle Triangle
To Prove:- Square of the hypotenuse is equal to the sum of the squares of the other two sides
Let ΔAOB be right angle triangle with right angle at O
Thus we have to prove
AB2 = OA2 + OB2
Proof: - Let, O at Origin, then
Since OB is perpendicular at OA
Therefore their Dot product is zero
)
⇒
⇒ ……(i)
Now,
⇒
From equation (i)
⇒
⇒ (Pythagoras theorem)
Hence, proved.